The present invention relates to methods of analysis. It is particularly, but not exclusively, concerned with methods of analysing test and/or service data, and more particularly such data from engines.
Analysis of the performance of gas turbine engines is important for both testing of development engines and condition monitoring of operating engines. In particular, the ability to identify accurately and reliably the component or components responsible for a loss of performance is beneficial. However, the nature of a gas turbine means there are inherent problems to be addressed if this is to be achieved in practice.
In common with other power plant, a gas turbine's performance can be expressed in terms of a series of performance parameters for the various components of the system. Typically, those chosen to characterise the performance of a gas turbine would be the efficiency and flow function of compressors and turbines and the discharge coefficient of nozzles. Significantly, these performance parameters are not directly measurable. They are, however, related to measurable engine parameters, such as spool speeds, averaged pressures and temperatures, thrust and air flows, and any loss in performance of a component will be reflected by changes in these measurable parameters.
Given a particular operating point, typically defined by environmental conditions and a power setting (inlet temperature and pressure, and fuel flow for example, or other such operating parameters), the relationship between measured engine parameters and performance parameters can be represented, for example, in a performance simulation model describing the aerothermodynamics of the gas turbine's components. In principle this enables the performance parameters, and more importantly changes in them from respective reference values, to be calculated. In turn, it should be possible, from these calculated values, to detect a drop in the performance of one or more components and hence deduce the cause of a loss in performance. This can be achieved using thermodynamic or synthesis models or by use of exchange rate models. Exchange rate models provide a linear relationship between performance and measurable engine parameters which is valid for small variations around the chosen operating point.
A number of methods exist for the understanding of engine test data produced from steady state engine analysis. The most basic of these uses measured engine parameters to calculate component thermodynamic efficiencies (actual gas temperature ratio across the component, relative to the ideal temperature ratio for the given pressure ratio). This provides component data at the conditions under which the test is run, but does not provide data which can be scaled or synthesised to other conditions. Additional parameters such as air flows and pressures and temperatures not measured directly (e.g. turbine entry temperature (TET): the gas temperature at the entry to the first (high pressure) turbine rotor blade, which is too hot to measure directly) may be calculated using further assumptions.
More rigorous analysis is possible using a tool known as ANSYN (“Analysis/Synthesis”) produced by Rolls-Royce. This uses a thermodynamic or synthesis model of the engine and thereby derives the scaling of characteristics etc. to match the measured data. This tool uses an iterative solution matching process whereby the user selects a number of parameters (e.g. efficiencies, flow capacities) that will be changed so as to match the measured data. An exact solution can therefore be obtained which can then be used to tune the model.
However, in the ANSYN tool, the number of variables must be equal to the number of measurements, as otherwise an exact solution cannot be obtained. Furthermore, this method can only provide a solution for those variables which are selected by the user and cannot analyse errors arising due to instrument inaccuracy or due to engine faults or divergences not covered by the selected variables (e.g. air system leakages).
For fault analysis, a program called AJA3 produced by Rolls-Royce is available. This program takes chosen parameters in turn and uses a least squares optimisation process and exchange rates to achieve a best match to the measured data. The parameter or parameters that give the best fit are then listed. This program can therefore be used to try to identify the causes of faults, but is time consuming to set up and has not been greatly used.
Other techniques for analysing test data have been studied recently. In particular, as described in U.S. Pat. No. 6,606,580 a genetic algorithm has been evaluated for solving least absolute error functions in an attempt to identify fault causes. The genetic algorithm makes use of a computer synthesis model and a number of variables to find a best fit to the measured data. The genetic algorithm itself is an iterative process that considers a large number of potential solutions at each iteration. From these solutions, the best are selected and developed into another set of possible solutions and the process repeated. This method permits the evaluation of instrumentation errors and is not limited in terms of the number of variables equalling the number of measurements. However, this process is very demanding in terms of the computing power and runs can take up to 12 hours to complete. It is also time consuming to set up.
Another tool available and used in engine trend monitoring is the module performance analysis (MPA) tool which forms part of “COMPASS”/VQ48 software produced by Rolls-Royce and discussed in GB 2,211,965. This uses a Kalman filter with a least squares optimisation scheme. The analysis is carried out using exchange rates rather than a synthesis model. The use of exchange rates can greatly simplify the analysis of engine data since the complicated thermodynamic relationships of a synthesis model are replaced by linear relationships between all of the parameters. Although exchange rate models are generally only applicable in situations where the values of the parameters change by small percentages (e.g. 3-4%), this is usually sufficient for this type of analysis.
This process permits measurement errors and component differences to be assessed. The assumption is made that measurement errors and component differences can be considered as statistical; that is, they are known with a particular uncertainty. More specifically, an optimisation can be carried out on the following function:
            ∑              i        =        1            n        ⁢                                                Var            ⁡                          (              i              )                                /                      VNorm            ⁡                          (              i              )                                                  2        +            ∑              j        =        1            m        ⁢                                                (                                          Mcal                ⁡                                  (                  j                  )                                            -                              M                ⁡                                  (                  j                  )                                                      )                    /                      MNorm            ⁡                          (              j              )                                                  2      where:Var(i) is the value of the ith variable; VNorm(i) is the normalisation value of the ith variable (if zero this variable is excluded from the error function); n is the number of variables; Mcal(j) is the matching value calculated from the exchange rates and the variable values for the jth matching quantity:
      Mcal    ⁡          (      j      )        =            ∑              i        =        1            n        ⁢                  Var        ⁡                  (          i          )                    ×              Xrate        ⁡                  (                      i            ,            j                    )                    where Xrate(i,j) is the exchange rate in the jth matching value with respect to the ith variable; M(j) is the measured value for the jth matching parameter; MNorm(j) is the normalisation value of the jth matching value (if this is zero, this matching value is not included in the error function; and Ef(j) is the error function type for the jth matching value with the same restrictions as Ef(i).
The solution that will minimise the amount of the error implied in the measurements and component changes is obtained. Further filtering may then be carried out which sets those errors that are smallest to be equal to zero and so concentrate the errors on fewer measurements and/or components. However, the use of the least squares optimisation results in the changes being shared across a large number of variables, resulting in both a reduction in the apparent magnitude of the correct parameters and “smearing” into parameters that should not have been affected. Additionally, the least squares approach is not statistically valid in the case where a fault exists (and under such circumstances this process will often fail completely). This is due to the statistical assumption that there is a normal distribution centred about the expected value. An error (such as that caused by a broken pipe or wire) will form a different statistic to that assumed to be due to random scatter (i.e. measurement accuracy).